The [1]} microphysical shock models depend only on
the number density of hydrogen protons \(n_0\)  and the velocity \(v_0\) , both evaluated immediately before the shock. Thus \(v_0=v(R_{\mathrm {p}})\)  from Equation (REF ) and \(n_0=X\rho (R_{\mathrm {p}})/m_\mathrm {H}\)  from Equation (REF ), where \(X\)  is the hydrogen mass fraction and \(m_\mathrm {H}\)  is the hydrogen atomic mass.
The number ratios are given by
\(\textrm {H}:\textrm {He}:\textrm {C}:\textrm {O}=1:10^{-1.07}:10^{-3.48}:10^{-3.18}\)  [2]}.
The present iteration of the models [1]} covers a range \(n_0=10^9\) –\(10^{14}\)  cm\(^{-3}\)  and \(v_0=20\) –200 \(\mathrm {km}\,\mathrm {s^{-1}}\) .
